Google displays the author of content in certain search results. They are doing this to help eliminate content farms. Google also mentioned they will be favouring pages with an author for their rankings calculation.
This article explains to setup authorship on your web pages
You should read about authorship in Google's webmaster tools help because there are a number of different ways you can implement authorship. (For example: by email)
First you need a Google+ profile. The Google+ profile is used to verify your a contributor at a website, as well as get your picture. Google+ requests you have a head shot, so if your avatar is not working try getting a picture of your face. You also want to make sure your author link text matches your Google+ name.
Next you need to setup the author link on your website. To do this, link to your author page using rel="author" (link must be on same domain). Next from your author page link to your Google+ account using rel="me".
To test your setup you can go to Google's Structured Data Page to ensure your code is correct.
If you can't use rel attribute, you can use the ?rel=author in your a tag. Here is Google's updated video about the url parameter.